Multi-linear multipliers associated to simplexes of arbitrary length

Details Multi-linear multipliers associated to simplexes of arbitrary length Multi-linear multipliers associated to simplexes of arbitrary length

2007-12-14

arxiv.org/abs/0712.2420v1

Mathematics

Classical Analysis and ODEs

52 pages, 6 figures

Scientific paper

In this article we prove that the $n$-linear operator whose symbol is the characteristic function of the simplex $\Delta_n = \xi_1 < ... < \xi_n$ is bounded from $L^2 \times ... \times L^2$ into $L^{2/n}$, generalizing in this way our previous work on the "bi-est" operator (which corresponds to the case $n=3$) as well as Lacey-Thiele theorem on the bi-linear Hilbert transform (which corresponds to the case $n=2$).

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